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arXiv:1609.04687 · Condensed Matter Physics

Bethe approach study of the mixed spin-1/2 and spin-5/2 Ising system in the presence of an applied magnetic field

Karimou, Yessoufou, Toussaint Djidjoho Oke, Kpadonou, Hontinfinde

Published Sep 1, 2016• 24 citations
arXivHTMLPDF

Abstract

The mixed spin-1/2 and spin-5/2 Ising model is investigated on the Bethe lattice in the presence of a magnetic field h via the recursion relations method.A ground-state phase diagram is constructed which may be needful to explore important regions of the temperature phase diagrams of a model.The order-parameters, the corresponding response functions and internal energy are thoroughly investigated in order to typify the nature of the phase transition and to get the corresponding temperatures.So, in the absence of the magnetic field, the temperature phase diagrams are displayed in the case of an equal crystal-field on the (k B T /|J |, D/|J |) plane when q = 3, 4, 5 and 6.The model only exhibits the second-order phase transition for appropriate values of physical parameters of a model.

DOI
10.5488/cmp.19.33003

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The mixed spin-1/2 and spin-5/2 Ising model is investigated on the Bethe lattice in the presence of a magnetic field h via the recursion relations method.A ground-state phase diagram is constructed which may be needful to explore important regions of the temperature phase diagrams of a model.The order-parameters, the corresponding response functions and internal energy are thoroughly investigated in order to typify the nature of the phase transition and to get the corresponding temperatures.So, in the absence of the magnetic field, the temperature phase diagrams are displayed in the case of an equal crystal-field on the (k B T /|J |, D/|J |) plane when q = 3, 4, 5 and 6.The model only exhibits the second-order phase transition for appropriate values of physical parameters of a model.
The mixed spin-7/2 and spin-1/2 Ising model with a crystal field in the absence and presence of an external longitudinal magnetic field is investigated within the framework both of the renormalization group (RG) method and Monte Carlo simulation (MCS). First, we have determined the ground-state phase diagram. Then, using RG technique, the finite temperature phase diagrams of this model are plotted for the two- and three-dimensional cases by following the flow in the parameters space of the Hamiltonian and evaluating the free energy and its isotherm derivative at low temperatures. Our results show that the model exhibits first- and second-order phase transitions as well as critical end-points. In addition, by linearizing the RG transformation at the vicinity of the fixed points of the second-order transition, we have determined the critical exponents. The MCS is also employed to validate the results obtained previously by renormalization, and to examine the influence of an external magnetic field on the magnetic properties and hysteresis loops of the system.
A bilayer Ising model consisting of two Bethe lattices, each of which is coupled with crystal fields of different strengths and each with a branching ratio of q Ising spins with one of the layers having only spin-1 and the other having only spin-3/2, is laid over the top of the other and the two layers are tied together via an interaction between the vertically aligned spins. After obtaining the ground-state (GS) phase diagrams on different possible planes depending on the given system parameters, the changes in the order-parameters and the free energy are investigated by use of the exact recursion relations in a pairwise approach to calculate the phase diagrams of the model. The ferromagnetic ordering in each of the layers and ferromagnetic or antiferromagnetic ordering of the adjacent nearest-neighbor (NN) spins of the layers are considered. The system presents both second- and first-order phase transitions. The lines of the first-order phase transitions end on either the stable or unstable tricritical points or at the isolated critical points. The model also displays one or two compensation temperatures when the bilinear interaction of the upper layer with spin-1 can compete with that of the lower layers with spin-3/2.
The phase diagrams of spin-1/2 Ising model on a two-layer Bethe lattice with antiferromagnetic interactions for each layer and either antiferromagnetic or ferromagnetic interaction between the layers are investigated by using the pairwise approach for given values of coordination number q.The exact expressions of the order--parameters, response functions and free energy are obtained in terms of the recursion relations.The ground-state phase diagrams are calculated for given system parameters of the model.In the guidance of the ground-state phase diagrams, the temperature dependent phase diagrams of the model are also studied in detail for given coordination numbers q = 3, 4 and 6.It was found that the system presents only second-order phase transitions with different thermal behaviors for all values of q.In addition, two Néel temperatures, T N , are found for q = 6 only.
Two-layer Bethe lattice whose lattice sites are occupied with spin-3/2 atoms is solved exactly by using the recursion relations in a pairwise approach for given coordination numbers q = 3, 4 and 6 with equal external magnetic fields acting on the layers.The ferromagnetic (FM) and antiferromagnetic (AFM) interactions for the spins of the upper and lower layers, respectively, and either FM or AFM type interactions between the adjacent spins of the layers are assumed.The phase diagrams of the model are studied on different planes for given system parameters by obtaining the ground state (GS) phase diagrams and the thermal variations of the order parameters and the response functions, i. e. the susceptibility and the specific heat, in detail.It was found that the model presents both second-and first-order phase transitions.The reentrant behavior is seen when the model presents two N éel temperatures for higher q values.The existence of the tricritical point and critical end points is also confirmed.
Phase diagrams and the thermal variations of the order‐parameters in the mixed spin‐1 and spin‐323 \over 223​ ising model on the Bethe lattice
Abstract The mixed spin‐1 and spin‐323 \over 223​ Blume‐Capel Ising ferromagnetic system (J > 0) with two crystal‐field interactions, DA for spin‐1 and DB for spin‐323 \over 223​, is studied on the Bethe lattice using the exact recursion equations for the central‐spin with spin‐323 \over 223​. The exact expressions for the order‐parameters, the Curie temperature and the free energy are obtained in terms of the recursion relations. The phase diagrams on the (kTcJ, DAJ)\bigg ({{kT_c}\over{J}}, \,{{D_A}\over{J}}\bigg )(JkTc​​,JDA​​) and (kTcJ, DBJ)\bigg ({{kT_c}\over{J}}, \,{{D_B}\over{J}}\bigg )(JkTc​​,JDB​​) planes are studied for selected values of DB/J and DA/J, respectively, for the coordination numbers q = 3, 4, and 6. Besides the second‐order phase transition lines, the lines of the first‐order phase transitions terminating either at a tricritical point or at an isolated critical point are found. The thermal variations of the order‐parameters are studied with two formulations, both obtained on the Bethe lattice for the mixed spin‐1 and spin‐323 \over 223​ Ising system using the exact recursion relations, but one with the central‐spin with spin‐1 and the other is for the central‐spin with spin‐323 \over 223​ for q = 3, thus, it is shown that the choice of the central‐spin on the Bethe lattice has no effect on the phase diagrams.
The spin-3/2 Ising model is investigated for the case of antiferromagnetic (AFM/AFM) interactions on the two-layer Bethe lattice by using the exact recursion relations in the pairwise approach for given coordination numbers q = 3, 4 and 6 when the layers are under the influences of equal external magnetic and equal crystal fields. The ground state (GS) phase diagrams are obtained on the different planes in detail and then the temperature-dependent phase diagrams of the system are calculated accordingly. It is observed that the system presents both second- and first-order phase transitions for all q , therefore, tricritical points. It is also found that the system exhibits double-critical end points and isolated points. The model also presents two Néel temperatures, T N , and the existence of which leads to the reentrant behaviour.